Fate of false vacuum in non-perturbative regimes: Gravity effects

A recent analysis of the false-vacuum decay in non-perturbative regimes is here extended in the presence of Einstein gravity, computing the corresponding effective potential and decay rate. We consider a $\lambda \phi^4$ scalar field theory and we observe that, in comparison to the usual perturbative decay rate, the higher the coupling $\lambda$, the greater the decay probability. We evaluate the running of the self-interaction coupling and obtain a weakly coupled theory at lower energies, proving that Einstein gravity grants an even more reliable weak coupling approximation with the universe cooling down. We also provide an extended study of a non-minimal coupling $\xi$ of the scalar field with gravity showing how this term makes the false-vacuum decay more difficult. Minima can also disappear at large coupling $\xi$. We discuss possible applications of these results to cosmological phase transitions, gravitational-wave astronomy, and condensed matter systems.